Age numbers are central, but it's pretty clear she's using them as a lattice to build, piece by piece, by induction, an entire model of arithmetic.
My theory is that she was initially too young, cognitively in the Piaget sense, to learn arithmetic deductively the way an older kid would (essentially "between any two numbers there exists a fixed interval; adding the interval to the smaller yields the larger; subtracting it from the larger yields the smaller; the intervals can be derived recursively from counting and smaller additions and subtractions").
Instead, Aviva has built up a neural net of arithmetic, narratively, by telling lots of stories of the form "when I am eight and Noah is five and Marie is seven and Goa is six and Daddy is thirty-nine and..."
The neural net initially had lots of funny holes, and didn't expand easily to varying contexts (e.g. she knew how old 3 years older than 16 was, but not necessarily how heavy three pounds heavier than 16lbs was), but now it has grown to where it more or less encompasses a dense set of single-digit addition and subtraction operations on any double-digit number...